Transfer Kernel And Interval-valued Hesitant Fuzzy Soft Sets And Their Applications In Decision-making

Fuzzy decision making is widely used to solve many practical problems,which fuzzy clustering analysis and fuzzy mult-attribute decision making are the two commonly used effective methods.The key to the application of system clustering method in fuzzy clustering analysis is to construct fuzzy equivalent matrix,and to calculate the transitive kernel of fuzzy matrix is an effective way to get fuzzy equivalent matrix.According to the decomposition theorem of fuzzy set theory,the core of solving the computational problem of fuzzy matrix transitive kernel is to master the calculation method of the Boolean matrix transitive kernel.On the basis of investigating the relevant literature at home and abroad and studying the properties of the Boolean matrix,the construction and algorithms of the Boolean matrix transitive kernel are carried out.Interval-valued hesitant fuzzy soft set is widely applied to solve fuzzy multi-attribute problems,because it can comprehensively and flexibly describe decision-makers' opinions and fully consider all kinds of parameters.Based on the analysis of the limitations of existing multi-attribute decision making method on interval valued hesitant fuzzy soft sets,a new multi-attribute decision making method based on interval valued hesitant fuzzy soft set is proposed,which is applied to evaluate the importance of major components of PDM.The main work and research results of this paper are as follows:1.On the basis of studying the structure characteristics of the transitive Boolean matrix,we obtain the important properties of the intersection matrix of a kind of special transitive Boolean Matrices.2.We obtain several kinds of rapid construction methods for the special transfer of Boolean matrix transitive kernel.3.After studying the calculation method of the general Boolean matrix transitive kernel,we proposed a theoretical algorithm.4.In view of the shortcomings of interval valued hesitant fuzzy element comparison law based on score function,combined with the characteristic function of interval valued,we proposed a comparative law of interval-valued hesitant fuzzy elements based on the possibility degree.5.We redefined some related concepts of interval valued hesitant fuzzy soft sets based on the comparative law of interval-valued hesitant fuzzy elements based on the possibility degree.6.The combination of interval valued hesitant fuzzy soft sets and the comparative law of interval-valued hesitant fuzzy elements based on the possibility degree,we proposed a new multi-attribute decision making method based on interval valued hesitant fuzzy soft sets.7.The method is applied to evaluate the importance of major components of PDM.In order to minimize huge economic losses caused by equipment failure,comparing the existing multi-attribute decision making method,we verified the effectiveness and feasibility of the method in the paper.